Parametric audio output in air is produced by the introduction of sufficiently intense, audio-modulated ultrasonic signals into an air column. Self-demodulation, or down-conversion, occurs along the air column resulting in an audible acoustic signal. This process occurs because of the known physical principle that when two sound waves with different frequencies are radiated simultaneously in the same medium, a sound wave having a wave-form including the sum and difference of the two frequencies is produced by the interaction (parametric interaction) of the two sound waves. So, if the two original sound waves are ultrasonic waves and the difference between them is selected to be an audio frequency, an audible sound is generated by the parametric interaction.
However, the interaction is non-linear in an elastic medium such as air; and, due to the non-linearities in the air column down-conversion process, distortion is introduced in the acoustic output. The distortion can be quite severe; and 30% or greater distortion may be present. Lowering the ultrasonic modulation amplitude level lowers the distortion, but at the expense of creating both a lower output volume and a lower power efficiency for the loudspeaker system.
In 1965, Berktay formulated that the secondary resultant output (audible sound) from a parametric loudspeaker is proportional to the second time derivative of the square of the modulation envelope. It was shown by Berktay that the demodulated signal, p2(t), in the far-field is proportional to the second time derivative of the modulation envelope squared.
                                          p            2                    ⁡                      (            t            )                          ∝                                            ∂              2                                      ∂                              t                2                                              ⁡                      [                                          (                                  env                  ⁡                                      (                    t                    )                                                  )                            2                        ]                                              (                  Equation          ⁢                                          ⁢          1                )            This is called Berktay's far-field solution for a parametric acoustic array. Berktay looked at the far-field because the ultrasonic signals are no longer present there (by definition). The near-field demodulation produces the same audio signals, but there is also ultrasound present which must be included in a general solution. Since the near-field ultrasound isn't audible, it can be ignored when considering only audible output, and with this assumption, Berktay's solution is valid in the near-field too.
The earliest use of this relationship in distortion reduction for parametric loudspeakers in air was modulator designs for parametric loudspeakers developed in the mid 1980's. This advancement included the application of a square-root function to the modulation envelope. Applying the square root function to the modulation envelope compensates for the natural squaring function that distorts the envelope of a modulated sideband signal emitted to the air. It has been shown that processing using square-root functions applied to double-sideband signals can theoretically produce a low distortion system; but it has been found as a practical matter that this requires very large bandwidth, and actually in theory it can be at the cost of requiring infinite system and transducer bandwidth. Of course it is not generally considered practical to try and produce a device that has an infinite bandwidth capability, or that tries to emulate one. Further, the implementation of this processing scheme with a significant bandwidth means that it is possible that the otherwise inaudible ultrasonic primary frequencies can extend down into the audible range (on the lower sideband). It will be appreciated that this can cause new distortion which can be at least as bad as the distortion eliminated by the “infinite” bandwidth square-root pre-processing system.
Moreover, just lowering/limiting the modulation amplitude level to prevent this new source of distortion is not an entirely satisfactory solution. Although it reduces the distortion, it also reduces the efficiency of the parametric conversion process. Moreover, clipping the lower frequencies so that they do not extend down into the audible range mitigates the latter distortion problem, but re-introduces distortion into the audio signal produced by the parametric array as it disrupts the sum and differences from time to time as the bottom is filtered out in the lower sideband.
For this and other reasons, it has historically been deemed very difficult to produce a strong undistorted audio output from parametric loudspeakers. These problems at least in part arise due to the difficulty of correcting for the significant distortion created by the down-conversion of the ultrasonic waves in the air.
Furthermore, in one application the desired audio signal is amplitude modulated (AM) onto an ultrasonic carrier of 25 kHz to 60 kHz, then amplified, and applied to an ultrasonic transducer. The outer envelopes of the carrier wave, or sidebands, carry the audio signal. If the ultrasonic intensity is of sufficient amplitude, the air column will perform a demodulation or down-conversion over some length (the length depends, in part, on the carrier frequency and column shape). The modulation of the ultrasonic carrier with the audio signal takes place using additional modulation circuitry, which increases the complexity and cost of the parametric loudspeaker system. Moreover, the carrier signal can be quite intense in this implementation, in order to get the system to work well in producing the audible waveform in air.
Due at least in part to the requirements, difficulties, and problems discussed above, parametric loudspeaker systems have been developed that pre-process the audio signal or modulated signal to allow a reduced distortion audio output to be heard after demodulation in the air. The first part of the processing is the modulation of the ultrasonic signal by the audio signal. An audio signal covers a range of approximately 20 Hz to 20 kHz. To produce a modulated ultrasonic signal a carrier frequency must be modulated with an audio signal of a lower frequency. For example, a 35 kHz signal might be used as the ultrasonic carrier and modulated with the original audio signal (e.g., a 10 kHz audio signal). This provides a new double sideband bandwidth of 25 kHz to 45 kHz which is in the ultrasonic range. This modulation can be performed using analog circuitry or digital signal processing, but this extra modulation circuit increases the cost of the overall parametric audio system as compared to conventional loudspeakers.
Another part of the pre-processing that can take place is the distortion correction. The distortion correction can include applying a square root to the signal to compensate for the second order distortion. This square root process can be applied to the audio input signal and/or an iterative envelope matching correction can be applied to the modulated signal to compensate for the second order distortion as predicted by the Berktay equation. These correction methods are described in detail in U.S. Pat. No. 6,584,205 entitled “Modulator Processing for a Parametric Loudspeaker System” filed on Aug. 26, 1999 and International Patent No. PCT/US00/23392 with the same title, which are hereby incorporated by reference. This distortion correction produces significant processing overhead especially if it is done iteratively. A considerable additional cost is also incurred because a signal processing chip or analog circuitry must be included in the speaker system to perform this function.
In short, these additional costs of implementing parametric systems generally within the audio industry continue to impede acceptance of parametric sound systems in day to day applications. This occurs despite the fact that parametric speakers offer unique advantages of directionality far exceeding that of conventional audio systems.